This is probably a spoiler ...

There are, I believe, eight possible answers where the product is 36 and the sum might be a house number. For six of those possibilities, the sum is unique; that is, the house number and product would be enough to completely determine the childrens' ages. Because that was NOT enough information, those six can be eliminated, narrowing it down to two. Of those two the finals statement is required to distinguish them.

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